G0444 is a preventive service, meaning there is no cost to the patient for the service. Likewise with the AWVs G0438 and G0439.
You cannot bill G0438 + G0444 because G0438 is the more extensive procedure and is never allowed. You can, however, bill G0444 with G0439 as the subsequent AWVs are less extensive.
When you bill G0444 with an office visit, the patient will end up with a bill because of the office visit charge. It's generally frowned upon, especially if the patient doesn't realize the visit is not completely preventive, meaning at no charge.
"Include an E/M code if your provider needs to treat the patient for a specific diagnosis during the visit and performs and documents the work associated with a problem oriented E/M service. Report the appropriate E/M code with modifier 25, Significant, separately identifiable evaluation and management service by the same provider on the same day of the procedure or other service, along with the supporting diagnosis, plus the wellness visit code.
The purpose of the AWV is to provide a preventive planning service, not take care of problems the patient has at the same time. As per the federal register, problems are to be addressed at a different visit, except when there is a rare circumstance that warrants dealing with a problem at the time of the AWV. Payers may allow billing a problem E/M service along with modifier 25."
Although it's allowed, personally I'm not a huge fan of lumping office visits and AWVs together. The AWV is at no cost to the patient; the depression screening is at no cost to the patient; the office visit is not. And I can't see the need to make it routine practice to do an office visit and an AWV together. It's not really "fair" to the patient in some ways.
On a side note, you can't add modifiers to the G codes. And mod 59 is not permitted on E/M codes.